Question

Equation of angle bisector of the lines 3x - 4y + 1 = 0 and 12x + 5y - 3 = 0 containing the point (1, 2) is

• A. 3x + 11y - 4 = 0
• B. 99x - 27y – 2 = 0
• C. 3x + 11y + 4 = 0
• D. 99x + 27y - 2 = 0

Answer 1

The correct option is B 99x - 27y – 2 = 0

We know that if the signs of equations substituted is opposite then we get the angle bisector containing the point using the -ve sign in the formula. Since $3\times 1-4\times 2+1$ and $12\times 1+5\times 2-3$ are of the opposite sign, so required angle bisector is given by
$\frac{3x-4y+1}{5}=-\left(\frac{12+5y-3}{13}\right)$